We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic prope...

The bulk distribution of the topological charge density, constructed via HP 1 σ-model embedding method, is investigated. We show that the existence of quadratic power correction to gluon condensate implies linear divergence of the non-perturbatively defined topological density in the continuum limit. As a consequence, the topologi-cal charge is to be distributed within three-dimensional sign-co...

We classify Bosonic Topological Insulators and Paramagnets in D ≤ 4 spatial dimensions using the cobordism approach. For D < 4 we confirm that the only such phase which does not fit into the group cohomology classification is the 3D Bosonic Topological Insulator protected by time-reversal symmetry whose surface admits an all-fermion topologically ordered state. ForD = 4 there is a unique ”beyon...

The line bundles which arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the Borel-Weil-Bott theorem of the representation theory. The remarkable relation of the geometric phase to the classification of complex line bundles provides the necessary tools for establishing the relevance of the Borel-Weil-Bott theorem t...

We give conditions on the numbers {φij} under which a vertexdegree-based topological index TI of the form

Let G be a graph and let mij(G), i, j ≥ 1, be the number of edges uv of G such that {dv(G), du(G)} = {i, j}. TheM -polynomial ofG is introduced withM(G;x, y) = ∑ i≤j mij(G)x y . It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the M -polyn...

The current work introduces an algorithm for constructing Reeb graph for CAD models and their inner cavities. The nodes of the graph represent areas of the manifold of the model where topological changes occur. Edges of the graph encode information about connections between such areas. The outline for the topological graph matching is given for detection of graph (sub)isomorphism. The proposed ...

We investigate topological properties of a completely integrable system on S× S × S which was recently shown to have a Lagrangian fiber diffeomorphic to RP 3 not displaceable by a Hamiltonian isotopy [Oakley J., Ph.D. Thesis, University of Georgia, 2014]. This system can be viewed as integrating the determinant, or alternatively, as integrating a classical Heisenberg spin chain. We show that th...

In this paper, we describe a technique, with roots in topological graph theory, that we call rind modeling. It provides for the easy creation of surfaces resembling peeled and punctured rinds. We show how the method’s two main steps of 1) creation of a shell or crust like the rind of an orange, and 2) opening holes in the crust by punching or peeling can be encapsulated into a real time semi-au...